CAIRO, July 28 (Reuters) - The United States urged Arab allyEgypt to pull "back from the brink" after security forces killeddozens of supporters of deposed Islamist President Mohamed Mursiand opened a dangerous new phase in the army's confrontationwith his Muslim Brotherhood.

Thousands of Brotherhood supporters were hunkered down in avigil at a Cairo mosque on Sunday, vowing to stand their grounddespite the imminent threat of a move to disperse them.

Saturday's bloodshed, following huge rival rallies, plungedthe Arab world's most populous country deeper into turmoilfollowing two turbulent years of transition to democracy withthe fall of veteran autocrat Hosni Mubarak in 2011.

Egypt's Health Ministry said 65 people had died. TheBrotherhood said another 61 were on life support after what itdescribed as a ferocious dawn assault by men in helmets andblack police fatigues. The ambulance service put the death tollat 72.

Bodies wrapped in white sheets were laid on the floor of aBrotherhood morgue, their names scrawled on the shrouds.

Washington, treading a fine line with an important MiddleEast ally and recipient of over $1 billion in military aid,urged the Egyptian security forces to respect the right topeaceful protest.

U.S. Defence Secretary Chuck Hagel spoke by telephone withEgyptian army chief General Abdel Fattah al-Sisi, who led theJuly 3 military overthrow of Mursi and whose face has appearedon posters across the teeming capital, Cairo.

U.S. Secretary of State John Kerry spoke to two seniormembers of Egypt's army-installed interim cabinet, expressinghis "deep concern."

"This is a pivotal moment for Egypt," he said in astatement. "The United States ... calls on all of Egypt'sleaders across the political spectrum to act immediately to helptheir country take a step back from the brink."

Saturday's violence, and the threat of more, has deepenedalarm in the West over events in the country of 84 millionpeople, a vital bridge between the Middle East and North Africa.

Over 200 people have died in violence since Sisi deposedMursi on the back of huge popular protests against his rule,ending a one-year experiment in government by the MuslimBrotherhood after decades spent in the shadows under successiveEgyptian strongmen.

PLEDGE TO STAY

The killings followed a day of rival mass rallies, triggeredby a call from Sisi for a popular mandate to confront "violenceand terrorism."

A public prosecutor is reviewing complaints from localresidents unhappy with the huge encampment on their doorstep.

Ibrahim said angry residents had clashed with Brotherhoodprotesters in the early hours of Saturday, and police intervenedwith teargas.

Brotherhood activists said they would not be cowed andwarned of worse bloodshed if the security forces did not backdown. Thousands were packed into the area as night fell.

"We will stay here until we die, one by one," said AhmedAli, 24, as he helped treat casualties at a makeshift fieldhospital on Saturday.

Brotherhood spokesman Gehad El-Haddad said they would remainuntil their demands are met and Egypt's first freely electedpresident is reinstated. He accused Sisi of issuing a "clear,pre-determined order to kill."

Mursi has been held in army detention at an undisclosedlocation since he was deposed. Ibrahim said he would likely betransferred shortly to the same Cairo prison where Mubarak isnow held, after authorities launched an investigation of him oncharges including murder stemming from his 2011 escape from jailduring Egypt's Arab Spring uprising.

The European Union and major European powers condemnedSaturday's bloodshed, the second mass killing since Mursi'souster. On July 8, more than 50 Brotherhood supporters died whensecurity forces opened fire on them outside a Cairo barracks.

The events have led U.S. President Barack Obama last week todelay delivery of four F-16 fighter jets, part of some $1.5billion a year in mainly military aid from Washington to Cairo,though U.S. officials have indicated there will be no cut-off insupport to the pivotal ally.